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Here is all you need to know about absolute value or modulus

Absolute value is a unique concept in math and is an important topic to know in order to perform algebra, geometry, and higher mathematics. Let our tutors help you learn it clearly.

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Absolute value:

The absolute value (or modulus),|x| of a real number x is its non-negative value regardless of its sign.The absolute value of a number may be conceived of as its position on the real number line in relation to zero.Furthermore, the distance between two real numbers is the absolute value of their difference.

 

Here is all you need to know about absolute value or modulus

Absolute value is a unique concept in math and is an important topic to know in order to perform algebra, geometry, and higher mathematics. Let our tutors help you learn it clearly.

 

Top things to learn about absolute value from the online tutor:
 

  • Definition
  • Properties of absolute value
  • Sign of Absolute value
  • Uses and applications of absolute value
  • Absolute value and number lines
  • Absolute value of integers
  • Absolute value of equations
  • When absolute value is not the same as modus
  • Absolute value function

 

Frequently Asked Questions:

Question 1: What is absolute value?

Absolute value defines how far is the number from zero on the number line without taking direction into account. A number's absolute value is never negative.

 

Question 2: How to solve absolute value equations?

 

To solve the absolute value equations we follow following steps:


Step1: We remove the absolute value expression from the equation.


Step 2: Set the quantity on one side of the equation to + and the amount on the other side of the equation to -.


Step 3:Solve both equations and find the value of the unknown.


Step 4: We can check our result analytically or graphically.


Example: Solve x;


                       |5x+6| = 2


Step 1: We remove the absolute value expression from the equation.


Value already isolated.


        5x + 6 = 2 or 5x + 6 = -2


Step 2: Set the quantity on one side of the equation to + and the amount on the other side of the equation to -.


        5x + 6 = 2


         5x + 6 = -2


Step 3: Solve both equations and find the value of the unknown.


                      5x + 6 = 2


                          5x = 2-6 = -4


                            x = -4/5


And,                5x + 6 = -2


                         5x = -2-6 = -8


                            x = -8/5


Step 4: Checking solution


Put x= -4/5 in |5x + 6|=|5*(-4/5) + 6| = |-4+6| = 2 = R.H.S


Put x= -8/5 in |5*(-8/5) + 6|=|5*(-8/5) + 6| = |-8+6| = |-2| = 2 = R.H.S

 

Question 3: How to solve absolute value inequalities?

To solve the absolute value inequalities we have to follow the following steps:


Step 1: On the left side of the inequality, we isolate the absolute value statement.


Step 2: If the integer on the opposite side of the inequality symbol is negative, our equation has either no solution or all real numbers as solutions.To determine which of these instances applies, we look at the sign of each side of our inequality.We proceed to Step 3 if the number on the other side of the inequality sign is positive.


Step 3: By using a compound inequality, we may remove the absolute value bars.The sort of inequality sign in the problem will instruct us on how to construct the compound inequality.


We set up a "or" compound inequality if our problem includes a greater than sign .


If the absolute value of your variable is less than a number, we create a three-part compound inequality.


Step 4: We solve the inequality.


Example:


              |x + 3| - 5 < 8


Step 1: Isolate the absolute value


         |x + 3| - 5 < 8


              |x + 3|<8+5


         |x + 3|< 13


Step 2: Is there a negative value on the other side?


    No, 13 is a positive value. So, we continue with step 3.


Step 3: Setting up a compound inequality


We will create a three-part inequality since the inequality        sign in our problem is a less than sign


           -13< x + 3<13


Step 4: Solving for inequality


           -13< x + 3<13


              -13-3< x + 3-3<13-3


            -16< x <10

 

Math Questions Answers Pages

 

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